The sum of $5$ consecutive integers is $505$. What is the third number in this sequence?
Solution: Call the first number in the sequence $x$. The next integer in the sequence is $x + 1$ The sum of the $5$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505$ $5x + 10= 505$ $5x = 495$ $x = 99$ Since $x$ is the first number, $x + 2$ is the third integer. Thus, the third number in the sequence is $101$.